Modular Forms Associated to Theta Functions
Canadian mathematical bulletin, Tome 45 (2002) no. 2, pp. 257-264

Voir la notice de l'article provenant de la source Cambridge University Press

We use the theory of Jacobi-like forms to construct modular forms for a congruence subgroup of $\text{SL}\left( 2,\,\mathbb{R} \right)$ which can be expressed as linear combinations of products of certain theta functions.
DOI : 10.4153/CMB-2002-029-9
Mots-clés : 11F11, 11F27, 33D10
Lee, Min Ho. Modular Forms Associated to Theta Functions. Canadian mathematical bulletin, Tome 45 (2002) no. 2, pp. 257-264. doi: 10.4153/CMB-2002-029-9
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[1] [1] Belokolos, E., Bobenko, A., Enol’skii, V., Its, A. and Matveev, V., Algebro-geometric approach to nonlinear integrable equations. Springer-Verlag, Heidelberg, 1994. Google Scholar

[2] [2] Borcherds, R., Automorphic forms on Os+2;2(R) and infinite products. Invent. Math. 120 (1995), 120–1995. Google Scholar

[3] [3] Cohen, P., Manin, Y. and Zagier, D., Automorphic pseudodifferential operators. Algebraic aspects of nonlinear systems, Birkhäuser, Boston, 1997, 17–47. Google Scholar

[4] [4] Conway, J. and Sloane, N., Sphere packings, lattices and groups. third ed., Springer-Verlag, Heidelberg, 1999. Google Scholar

[5] [5] Dickey, L., Soliton equations and Hamiltonian systems. World Scientific, Singapore, 1991. Google Scholar

[6] [6] Dong, C. and Mason, G., Transformation laws for theta functions. Preprint (math.QA/9903107). Google Scholar

[7] [7] Ebeling, W., Lattices and codes. Vieweg, Braunschweig, 1994. Google Scholar

[8] [8] Eichler, M. and Zagier, D., The theory of Jacobi forms. Progress in Math. 55, Birkhäuser, Boston, 1985. Google Scholar

[9] [9] Mumford, D., Tata lectures on theta II. Birkhäuser, Boston, 1984. Google Scholar

[10] [10] Schoeneberg, B., Elliptic modular functions. Springer-Verlag, Heidelberg, 1974. Google Scholar

[11] [11] Zagier, D., Introduction to modular forms. From number theory to physics (eds., M.Waldschmidt, P. Moussa, J. Luck and C. Itzykson), Springer-Verlag, Heidelberg, 1992, 238–291. Google Scholar

[12] [12] Zagier, D., Modular forms and differential operators. Proc. Indian Acad. Sci. Math. Sci. 104 (1994), 104–1994. Google Scholar

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